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Microcausality: How does modular manipulation of public opinion work using the Dirac Field?
- The article discusses the theory behind microcausality and its relation to using the Dirac Field to manipulate public opinion.
- The theory of microcausality involves analyzing partial differential operators for future-directed timelike unit vectors and spacelike unit vectors.
- The Fourier transform of the Klein-Gordon equation, which describes particles in 1 + 1 dimensions, is used to model classical relativistic particles with positive-energy vectors.
- The bosonic Fock space H is used to define quantum fields by replacing complex field values with linear operators in an infinite-dimensional Hilbert space.
- The finite-particle space D, constructed from wave functions, is used to distinguish between zero-particle and N-particle spaces.
- Annihilation operators can be defined for sharp momenta, but their hermitian adjoints are ill-defined as operators.
- Creation and annihilation operators are unbounded and exhibit the commutation relation, allowing for the definition of the scalar field as a C-linear distribution.
- The hermitian scalar field of mass m can be defined by the distribution equation in (8), which describes the spacelike separation of field operators.
- The consequence of this separation is called microcausality, which implies that field operators located in spacelike separated regions must commute for the hermitian scalar field.
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